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Alternating Current Circuits - General Physcis - Lecture Slides, Slides of Physics

University of Allahabad Physics

General Physics is also known as everyday physics. Every topic in this course talks about any aspect of our daily routine and observations. Objective of the course is to increase student's interest in physics. Key words in this course are: Alternating Current Circuits, Alternating Current, Current Elements in Ac Circuits, Lc Circuits, Driven RLC Circuits and Resonance, Power in AC Circuits, Transformers, Power Supplies, Induction, Transformation

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28. Alternating Current Circuits

1. Alternating Current

2. Current Elements in AC Circuits

3. LC Circuits

4. Driven RLC Circuits & Resonance

5. Power in AC Circuits

6. Transformers & Power Supplies

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Download Alternating Current Circuits - General Physcis - Lecture Slides and more Slides Physics in PDF only on Docsity!

28. Alternating Current Circuits

1. Alternating Current

2. Current Elements in AC Circuits

3. LC Circuits

4. Driven RLC Circuits & Resonance

5. Power in AC Circuits

6. Transformers & Power Supplies

Why does alternating current facilitate the transmission and distribution of electric power?

EM induction allows voltage transformation.

Example 28.1. Characterizing Household Voltage

Standard household wiring supplies 110 V rms at 60 Hz.

Express this mathematically, assuming the voltage is rising through 0 at t = 0.

V (^) p = 2 Vrms =^156 V

1 377 s

−

ω = 2 π f = 2 π ( 60 Hz ) =

V = V p sin ( ω t +φ)

V ( t = 0 ) = 0 → 0 = Vp sin^ φ

∴ φ = 0 V^ = V^ p sin^ ω t =156 sin 377( t ) V

28.2. Current Elements in AC Circuits

 Resistors

 Capacitors

 Inductors

 Phasor Diagrams

 Capacitors & Inductors: A Comparison

Resistors

V ( ) t

I

R

= sin

V (^) p t R

sin^ I^ &^ V^ in phase

I = I p ω t

p p

V

I

R

rms rms

V

I

R

+ VR −

I

−

V ( ) t − VR = 0 V^ p^ sin^ ω^ t^ −^ I R =^0

When V ( t ) > 0 :

Capacitors

q = C V ( ) t = C Vp^ sin^ ω t

d q I d t

= = C Vp ω cosω t

sin 2

I C V (^) p t

I leads V by 90°

I p = C Vp ω

V

X

X C

ω C

= (^) Capacitive reactance

[ X^ C ]= Ω

X C → ∞ as ω→ 0 DC: open ckt.

X C → 0 as ω→ ∞ HF: short ckt.

I peaks ¼ cycle before V

d V C d t

+ VC −

I

−

V ( ) t − VC = 0 p sin^0

q V t C

ω − =

When V ( t ) > 0 :

Table 28.1. Amplitude & Phase in Circuit Elements

Circuit Element Peak Current vs Voltage Phase Relation

Resistor

Capacitor

Inductor

p p

V

I

R

p p C

V

I

X

V p

ω C

p p L

V

I

X

ω L

V & I in phase

V lags I 90 °

V leads I 90 °

GOT IT? 28.1.

A capacitor and an inductor are connected across separate but identical electric generators,

and the same current flows in each.

If the frequency of the generators is doubled, which will carry more current?

I p C = V p ω C

p p L

V

I

ω L

Ans. is capacitor

I ′ p C^ = 2 Vp ω C

p p L

V

I

ω L

= 2 Ip C

= Ip L

Phasor Diagrams

Phasor = Arrow (vector) in complex plane. Length = mag. Angle = phase.

V leads I by 90°. V leads I by − 90 °.

( V lags I by 90 °)

V leads I by 0°.

( same phase )

V = I X

i V V e

φ

i t V e

ω

Capacitors Revisited

q = C V i t C V (^) p e

ω

d q I d t

i t C V (^) p i e

I leads V by 90°

dV C d t

+ VC −

Vp e i^ ω^ t

Taking the real part as physical

V = V p cos ω t

I = − CV (^) p ω sinω t cos 2

CV (^) p t

Taking the imaginary part as physical

V = V p sin ω t

I = CV p ω cosω t sin

CV (^) p t

I = i ω C V^2

i C V e

π =ω

V = I Z

Z i

ω C

= − (^) Impedance

I

Capacitors & Inductors: A Comparison

C ↔ L translator:

E ↔ B

q ↔ φ B

V ↔ I

Z ↔ Y

Table 28.2. Capacitors & Inductors

Capacitor Inductor

Behavior in low freq limit

Defining relation; differential form

Opposes change in

Energy storage

Defining relation

Behavior in high freq limit

Reactance

Phase

q C V

= L B

I

dV I C d t

d I V L d t

V I

U E = C V

U B = L I

Open circuit Short circuit

Short circuit Open circuit

I leads by 90° V^ leads by 90°

1 / X C = ω C X^ L =^ ω L

Admittance / Impedance (^) 1 /

YC = i ω C = ZC Z L = i ω L

28.3. LC Circuits

I

−

Analyzing the LC Circuit

U = U B + UE

= L I + C V

d U

d t

d I d V L I C V d t d t

q V C

d q I d t

2 0

d q q L d t C

q = q p cos ω t

L C

I

−

q d I L C d t

d I q d q L I d t C d t

d I q L d t C

Alternating Current Circuits - General Physcis - Lecture Slides, Slides of Physics

Related documents

Partial preview of the text

Download Alternating Current Circuits - General Physcis - Lecture Slides and more Slides Physics in PDF only on Docsity!

28. Alternating Current Circuits

1. Alternating Current

2. Current Elements in AC Circuits

3. LC Circuits

4. Driven RLC Circuits & Resonance

5. Power in AC Circuits

6. Transformers & Power Supplies

Example 28.1. Characterizing Household Voltage

ω = 2 π f = 2 π ( 60 Hz ) =

V = V p sin ( ω t +φ)

V ( t = 0 ) = 0 → 0 = Vp sin^ φ

∴ φ = 0 V^ = V^ p sin^ ω t =156 sin 377( t ) V

28.2. Current Elements in AC Circuits

Resistors

V ( ) t

I

R

I = I p ω t

V

I

R

V

I

R

I

V ( ) t − VR = 0 V^ p^ sin^ ω^ t^ −^ I R =^0

Capacitors

q = C V ( ) t = C Vp^ sin^ ω t

= = C Vp ω cosω t

I p = C Vp ω

V

X

X C

ω C

[ X^ C ]= Ω

X C → ∞ as ω→ 0 DC: open ckt.

X C → 0 as ω→ ∞ HF: short ckt.

I

V ( ) t − VC = 0 p sin^0

Table 28.1. Amplitude & Phase in Circuit Elements

V

I

R

V

I

X

ω C

V

I

X

ω L

GOT IT? 28.1.

I p C = V p ω C

V

I

ω L

I ′ p C^ = 2 Vp ω C

V

I

ω L

Phasor Diagrams

V = I X

φ

ω

Capacitors Revisited

ω

V = V p cos ω t

V = V p sin ω t

I = CV p ω cosω t sin

V = I Z

ω C

I

Capacitors & Inductors: A Comparison

E ↔ B

q ↔ φ B

V ↔ I